It is oftentimes desirable to determine the necessary capacity of a network, such as a communications network. For example, it is sometimes desirable to predict the desired capacity of a network, both currently and at times in the future, so that the network can be properly sized and designed. In this regard, it is useful for a network to have sufficient capacity to support all of the communications that are desired to be routed over the network, while maintaining a desired quality of service for the network traffic.
While a variety of different network topologies are in use and additional network topologies will be developed, one exemplary network is a network-centric system that provides bi-directional, high-speed broadband Internet data services for commercial airline passengers through shared broadband satellites in geosynchronous orbit. One example of such a system is depicted in FIG. 1 which illustrates an aircraft 10 in flight that is configured to communicate via the network. As shown, passengers onboard the aircraft can receive television and other media broadcast from a direct broadcast satellite (DBS) television service provider 12 via a DBS satellite 14. Additionally, passengers onboard the aircraft can communicate via the Internet, corporate Intranet, military secure nets and other network via a bi-directional data link supported by a network of satellites 16, such as a network of geosynchronous Ku-band satellites. As shown in FIG. 1, for example, the satellites can communicate both with the aircraft via a downlink and an uplink and with a ground station 18 in order to upload data from the ground station to the satellite and to download data from the satellite to the ground station. The ground station, in turn, can communicate, such as via a dedicated terrestrial circuit, with a network operations center 20 which, in turn, facilitates communication with any of a variety of other networks including, for example, the Internet. Among other functions, the network operations center provides network control to monitor service usage and to increase or decrease capacity in order to maintain a desired quality of service as user demand fluctuates.
In order to model network capacity, a measure of the network traffic must be obtained. For a network that is operational, network traffic can be collected by network sniffers, i.e., passive data monitoring units, that monitor, collect and analyze traffic header information as the network traffic passes along the network. With respect to the exemplary network depicted in FIG. 1, network sniffers may be positioned at various geographical locations to monitor network traffic in route to or from the ground stations 18. While the network sniffers can collect a variety of information representative of the network traffic, the network sniffers may collect real-time packet and bit rate information for both the forward and return links established between the ground station and the constellation of satellites 16.
Based upon the data representative of the network traffic that is collected by the network sniffers or otherwise, the network capacity can be modeled. A variety of modeling techniques have been developed including models which employ stochastic-based mathematical equations for aggregating network traffic and models based on quality of service admission controls. In addition to these methods, most current modeling techniques are designed to express network traffic as a function of fractional Brownian motion as proposed, for example, by Ilkka Norros in an article entitled “On the Use of Fractional Brownian Motion in the Theory of Connectionless Networks” published in the IEEE Journal on Selected Areas in Communications, Volume 13, No. 6, pages 953-62 (August 1995). The modeling of network traffic as a function of fractional Brownian motion is based upon two key assumptions, namely, self-similarity and long-range dependency. In this regard, the self-similarity characteristics of network traffic were reported by Will Leland, Maurad Taqqu, Walter Willinger, and Daniel Wilson. in an article (hereinafter the “Leland article”) entitled “On the Self-Similar Nature of Ethernet Traffic (Extended Version)” published in the IEEE/ACM Transactions on Networking, Volume 2, No. 1 (February 1994). Prior to the discovery of the self-similarity characteristics of network traffic, network traffic had been generally modeled as a Poisson process with the analysis based on the Poisson or Markov modulated distributions. However, network traffic tended to exhibit self-similarity which implies consistency over varying timesets. As described by Stefano Bregni in an article entitled “The Modified Allan Variance as Time-Domain Analysis Tool for Estimating the Hurst Parameter of Long-Range Dependent Traffic” in the proceedings of IEEE Communications Society, Globecom 2004 (December 2004), a self-similar random process is characterized by a dilated portion of a sample path having the same statistical characterization as the whole. In this regard, the dilation may be applied on one or both of the amplitude and time axes of the sample path. In this regard, bursty Internet traffic composed mostly of web surfing tends to be self-similar since network traffic that is burstier also tends to be closer to pure Brownian motion. By modeling network traffic as a function of fractal Brownian motion, the capacity of a network was generally determined in an algorithmic manner as a mathematical equation. In this regard, system bandwidth needs are generally approximated by the network link capacity. The network link capacity is, in turn, defined as the maximum rate for data transfer via the respective link. At a given instance in time, a link is either transmitting at capacity or is idle. The capacity of the network path consisting of N links, L1 . . . LN, is therefore defined as:
                              A          ⁡                      (                          t              ,                              Δ                ⁢                                                                  ⁢                t                                      )                          ⁢                                                                    ⁢            min                                i            =                          1              ⁢                                                          ⁢              …              ⁢                                                          ⁢              N                                      ⁢                  1                      Δ            ⁢                                                  ⁢            t                          ⁢                              ∫            t                          t              +                              Δ                ⁢                                                                  ⁢                t                                              ⁢                                                    C                i                            ⁡                              (                                  1                  -                                                            u                      i                                        ⁡                                          (                      τ                      )                                                                      )                                      ⁢                          ⅆ              τ                                                          (        1        )            where C1 . . . Cn, are link capacities and the values u1(t) . . . un(t) are percentages of link utilization, as described by Leopoldo Angrisani, Salvatore D'Antonio, Marcello Esposito, and Michele Vadursi in an article entitled “Techniques for Available Bandwidth Measurement in IP Networks: A Performance Comparison” in the Journal of Computer Network, Volume 50, pages 332-49 (2006).
Based on assumptions of self-similarity and fractional Brownian motion, a mathematical expression for a capacity of a network can be determined. In this regard, one mathematical expression for capacity in bits per second (BPS) is as follows:C=m+(κ(H)√{square root over (−2 ln(ε))})1/Ha1/(2H)B−(1-H)/Hm1/(2H)  (2)κ(H)=HH(1−H)(1-H)  (3)                wherein m=Mean Bit Rate (bps) per user                    a=Peakiness (bps)            ε=Cell Loss Rate            B=Buffer Size (bits)            H=Hurst Parameter            C=Capacity (bps)                        
The peakiness a, or variance coefficient, is closely related to the variance of the network traffic and is a measure of the magnitude of fluctuations within the network traffic. The cell loss rate ε is a constant sized for the system to be modeled. The buffer size B is derived from the peak capacity of the system and the maximum queuing delay. The Hurst parameter H is a measure of the rate of decay of correlations of arriving packets or bits over time. It is further noted that the mean bit rate m, the peakiness and the Hurst parameter H collectively comprise a measure of the self-similarity of the network traffic in the aggregate.
Although traditional approaches to modeling the capacity of a network have proven useful, conventional modeling techniques are challenged when complex, large-scale global networks are to be modeled. In this regard, the mathematical expression of the capacity, as exemplified by equation 2 above, may not be applicable throughout different locations of the network. Additionally, accuracy in the modeling of the capacity is dependent upon the exact characterization of the traffic stream, which is typically not very accurate. See William Cleveland, and Don Sun, “Internet Traffic Data”, Journal of the American Statistical Association, Volume 95, pages 979-85 (2000); Houjin Li, Changchen Huang, Michael Devetsikiotis, and Gerald Damm, “Effective Bandwidths Under Dynamic Weighted Round Robin Scheduling”, Proceedings of IEEE Communications Society, Globecom 2004 (December 2004); and Lie Qian, Anand Krishnamurthy, Yuke Want, Yiyan Tank, Philippe Dauchy, and Alberto Conte, “A New Traffic Model and Statistical Admission Control Algorithm for Providing QoS Guarantees to On-Line Traffic”, Proceedings of IEEE Communications Society, Globecom 2004 (December 2004).
Additionally, collecting, evaluating and constantly updating measured data from the network for input to the mathematical expression, such as for derivation of the various parameters utilized by the mathematical expression of capacity, may prove to be a tremendous challenge. In this regard, some data values may be quite difficult to extrapolate from the network traffic, especially the parameters relating to self-similarity and long-range dependency parameters such as the Hurst parameter and other self-similar characterizations. See Stefano Bregni, “The Modified Allan Variance as Time-Domain Analysis Tool for Estimating the Hurst Parameter of Long-Range Dependant Traffic”, Proceedings of IEEE Communications Society, Globecom 2004 (December 2004). Further, the network traffic may be in a state of constant change and evolution, thereby limiting the usefulness of the mathematically derived capacity of the network. Finally, the mathematical expressions utilized to model network traffic are based upon an assumption that the network traffic is self-similar which, in turn, limits the applicability of such modeling techniques.
The difficulties associated with efforts to characterize the basic nature of modern Internet traffic and the difficulties of accurately modeling a complex global network is exemplified by the variability of data characteristics exhibited by users of different applications. In this regard, an example of the data rate over time by email applications is depicted in FIG. 2, an example of the data rate over time of virtual private network (VPN) traffic is depicted in FIG. 3, an example of the data rate over time of web surfing traffic is depicted in FIG. 4, an example of the data rate over time of file transfer protocol (FTP) traffic is illustrated in FIG. 5, an example of the data rate over time of game applications is illustrated in FIG. 6 and an example of the data rate over time of Voice over Internet protocol (VoIP) traffic is illustrated in FIG. 7. The data rates vary greatly between the various applications.
Even among individual users, there is a great degree of variability. In this regard, FIG. 8 depicts a 0.1 hour (i.e., 6 minute) time segment of the network traffic for 18 users. Additionally, FIG. 9 depicts a 0.01 hour (i.e., 36 second) time segment to illustrate the difference between individual users on a more granular level. In FIGS. 8 and 9, each line represents the data rate demanded by a respective user over time.
On an even more individualized level, a single user can have different network demands at different points in time. In this regard, FIG. 10 illustrates the network usage of a single user over a 12-hour period, while FIG. 11 depicts the network usage of a single user over a 0.5 hour segment to provide additional details. As shown in FIGS. 10 and 11, the network usage includes dead time of inactivity of varying lengths, times of high and low burstiness and times of sustained relatively constant data rates. These changing characteristics are due to varying activities of the user, such as times of high or low activity, or times when the user is utilizing different applications, such as email applications, web surfing applications or streaming media applications. As such, not only are the demands of each user upon a network different, but the network usage characteristics of a single user vary over time. As will be appreciated, the variations in the network traffic characteristics based on circumstance, time and location and the constant evolution and change of those network traffic characteristics makes it very difficult, if not impossible, to model the network capacity with explicit mathematical expressions as has been utilized in the past since the prior models have generally provided point solutions that were not particularly adaptable or scalable. As such, it would be desirable to develop an approved technique for modeling network capacity, even in instances in which the network traffic characteristics change over time and may be different based on circumstance, time and location.